Perplexahedron (derived from "perplex", meaning to confuse and "hedron", a geometry term used in the name of solid figures) is an artificial cube shaped planet that held the fourth and final piece of the Map of Infinity. It's known for being a maze-like/cube-shaped labyrinth planet and leads people into the wrong paths, protecting the Map of Infinity from intruders.
Its doors will move to various places, leading people back to where they once started from. Its doors will also form into a guard to fight people who come intact, preventing them from moving on to the next room. It was revealed that for them to be called "Guards" they must be guarding something. It was evident that the guards would appear only to protect the Map of Infinity as you got closer to it. The only known inhabitant of this planet is The Sentinel.
It is similar to the Labyrinth in the Percy Jackson series, as the rooms constantly shift and change places and there are many traps and guards to protect its inner depths. It was destroyed when a piece of the Map of Infinity was given up by the Sentinel (and thus served its purpose).
The idea of perplexahedron is derived from the 1997 science fiction movie "Cube ". In the movie, a similar structure is created with identical rooms, some with lethal traps, to prevent its inhabitants from escaping. However, the white appearance of the rooms of perplexahedron is same as those of an older movie "The Cube " released in 1969.